Radiation by moving charges

It is generally accepted that in order to describe the dynamics of relativistic particles in the laboratory (lab) frame it is sufficient to take into account the relativistic dependence of the particle momenta on the velocity. This solution of the dynamics problem in the lab frame makes no reference to Lorentz transformations. For this reason they are not discussed in particle tracking calculations in accelerator and plasma physics. It is generally believed that the electrodynamics problem can be treated within the same ''single inertial frame'' description without reference to Lorentz transformations. In particular, in order to evaluate radiation fields arising from charged particles in motion we need to know their velocities and positions as a function of the lab frame time t. The relativistic motion of a particle in the lab frame is described by Newton's second law ''corrected'' for the relativistic dependence of momentum on velocity. It is assumed in all standard derivations that one can perform identification of the trajectories in the source part of the usual Maxwell's equations with the trajectories vector x(t) measured (or calculated by using the corrected Newton's second law) in the lab frame. This way of coupling fields and particles is considered since more than a century as the relativistically correct procedure.We argue that this procedure needs to be changed, and we demonstrate the following, completely counterintuitive statement: the results of conventional theory of radiation by relativistically moving charges are not consistent with the principle of relativity. In order to find the trajectory of a particle in the lab frame consistent with the usual Maxwell's equations, one needs to solve the dynamic equation inmanifestly covariant form by using the coordinate-independent proper time τ to parameterize the particle world-line in space-time. We show that there is a difference between ''true'' particle trajectory vector x(t) calculated or measured in the conventional way, and covariant particle trajectory vector x_cov(t) calculated by projecting the world line to the lab frame (t(τ),x₁(τ),x₂(τ),x₃(τ)) and using the lab time t to parameterize the trajectory curve. In other words, for a relativistic motion accelerated along a curved trajectory, the results of conventional particle tracking differ from those of covariant particle tracking. The difference is only due to a choice of convention, but only vector x_cov(t) is consistent with the usual Maxwell's equations. This essential point has never received attention in the physical community. As a result, a correction of the conventional synchrotron-cyclotron radiation theory is required.